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Summary - Unit Roots

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Empirical Finance

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Vrije Universiteit Amsterdam (VU)

This summary provides the basis for unit roots. It contains an explanation of the unit root issues, transitory effects, permanent effect, random walk model (with drift), trend stationary process, how to solve the issues, de-trending, how to formally test for non-stationarity, Dikey-Fuller test, A...

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Type Samenvatting

summary empirical finance
unit root
vu university
vrije university
opschoor
transitory effect
permanent effect
random walk model
dikey fuller test
interpretation
non stationary
results interpretation

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,For the Exam (What should we know)

- ARMA models
o Why do we do this?
o Estimate the ARMA models.
o Residuals
o Diagnostic checks
o Forecasting
o Forecasting evaluation

- GARCH Models
o Why do we use these models?
o Types of GARCH models, tries to capture autocorrelation in squared variables.
o Diagnostic checks
o Forecasting
o Forecasting with value at risk
o Evaluation by the means of High Frequency Data or by Value at Risk.
- Unit Roots
o What happens to an AR model or an ARMA model when we have a unit root.
o How can we get rid of it?

- The regression is highly significant. However, this seems to be much of a trend and in reality,
there is no connection between the two.
- If there is indeed a relationship between the two, then, if we take the growth rate (the
differences) of both variables, it should show us the same relationship.

,- If you regress the growth rate of both variables you will see that there is no significant
relationship among the two.

- This concept that you should be aware of, is called unit root.

- Based on the first picture, we are not allowed to run a regression because there is no
causality, it is a spurious regression.

- The whole reason why they go together is because they are part of a trend.

- Means and variance are assumed to be constant. Not conditionally, but unconditionally.
- Unconditional mean and unconditional variance should be constant. Otherwise, the t-
statistic is not good.

, - We must look at the data and check whether it is stationary or nonstationary.

Transitory effect: If there is a shock today it will have an effect tomorrow, and the day after
tomorrow, and so on. In the end, the effect will be 0.

- This happens only if we have stationary data.
- Stationary data means that the data goes many time through its own mean.
- This also means that unconditionally the mean is constant.
- If Φ1 = 1, then we will not have a transitory effect of the shock anymore, but it will have a
permanent effect, the series will not go back to its mean. Yt will be a sum of all the shocks.

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